Exercise 5.8

1. Examine whether the following are polygons. If any one among them is not, say why?
(i)
Figure (i)
Solution: It is not a closed figure. Hence, it is not a polygon.
(ii)
Figure (ii)
Solution: It is a polygon made of six sides.
(iii)
Figure (iii)
Solution: No, it is not a polygon because it is not made of line segments (it is a circle).
(iv)
Figure (iv)
Solution: It is not a polygon, as it is not entirely made of line segments (it has a curved part).
2. Name each polygon.
(a)
Polygon (a)
Solution: It is a closed figure and is made of four line segments. Hence, the given figure is a quadrilateral.
(b)
Polygon (b)
Solution: The given figure is a triangle, as it is a closed figure with 3 line segments.
(c)
Polygon (c)
Solution: The given figure is a pentagon, as the closed figure is made of 5 line segments.
(d)
Polygon (d)
Solution: The given figure is an octagon, as it is a closed figure made of 8 line segments.
3. Draw a rough sketch of a regular hexagon. Connecting any three of its vertices, draw a triangle. Identify the type of triangle you have drawn.
Regular Hexagon with Triangle
Solution: We can draw an isosceles triangle by joining three vertices of a hexagon, as shown in the above figure.
4. Draw a rough sketch of a regular octagon. (Use squared paper if you wish.) Draw a rectangle by joining exactly four of the vertices of the octagon.
Regular Octagon with Rectangle
Solution: The above figure is a regular octagon in which a rectangle is drawn by joining four of the vertices of the octagon.
5. A diagonal is a line segment that joins any two vertices of the polygon and is not a side of the polygon. Draw a rough sketch of a pentagon and draw its diagonals.
Pentagon with Diagonals
Solution: From the figure, we can find AC, AD, BD, BE and CE are the diagonals.